How does the curvature of the universe evolve in cyclic models?

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Discussion Overview

The discussion centers on the evolution of the curvature of the universe over time, particularly in the context of cyclic models and inflationary theory. Participants explore how the curvature parameter \(\Omega_k\) may have changed before and during inflation, as well as implications for cyclic models compared to traditional big bang scenarios.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the historical values of \(\Omega_k\) before inflation and its changes during inflation, noting the current observation of a nearly flat universe.
  • Another participant explains that \(\Omega_k\) changes with energy density as \(1/a^2\) and discusses how during matter domination, curvature becomes more significant as matter density dilutes, while during inflation, curvature dilutes away due to the energy density being nearly constant.
  • A third participant suggests that probing the universe's conditions before inflation remains largely unknowable, referencing WMAP as a tool for understanding the early universe, but noting the evidence is still tenuous.
  • A fourth participant contrasts the traditional big bang model with cyclic models, suggesting that cyclic models allow for a finite bang and potentially more information about the universe's curvature, referencing a book by Paul Steinhardt and Neil Turok.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the conditions of the universe before inflation, with some suggesting it is largely unknowable. There is a divergence in views between traditional big bang models and cyclic models, indicating multiple competing perspectives on the topic.

Contextual Notes

Limitations include the dependence on assumptions about the early universe and the challenges in probing conditions beyond the surface of last scattering. The discussion highlights unresolved aspects of curvature evolution and the implications of different cosmological models.

Who May Find This Useful

Readers interested in cosmology, particularly those exploring the implications of inflationary theory and cyclic models of the universe.

zeebo17
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How has the curvature of the universe changed with time?

I know that the universe is observed to nearly flat at the present time and that inflation was proposed (one of the reasons) to drive the universe to be almost perfectly flat. Do we have any idea what [tex]\Omega[/tex]k could have been like before inflation and how it changed during inflation?

Thanks!
 
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zeebo17 said:
How has the curvature of the universe changed with time?

I know that the universe is observed to nearly flat at the present time and that inflation was proposed (one of the reasons) to drive the universe to be almost perfectly flat. Do we have any idea what [tex]\Omega[/tex]k could have been like before inflation and how it changed during inflation?

Thanks!
Basically, the curvature portion [tex]\Omega_k[/tex] changes with the energy density as [tex]1/a^2[/tex]. So if, for instance, you are matter dominated, as matter dilutes as [tex]1/a^3[/tex], as the universe expands curvature becomes more and more important. By contrast, during inflation, our universe was dominated by some stuff that acted much like a cosmological constant, which means its energy density was nearly independent of the expansion. So as the expansion progressed during inflation, the curvature diluted away as [tex]1/a^2[/tex]. As a result, we can't really know what it was before inflation began, as inflation set it to be nearly identically zero due to the massive increase in [tex]a[/tex] during that time.
 
That remains mostly in the realm of the unknowable. Our best effort to probe beyond the surface of last scattering is WMAP. The evidence is still tenuous. If we assume the universe arose from a 'big bang', we are forced to assume something prevented it from either immediately collapsing, or expanding out of view.
.
 
In a one time big bang model, as noted, so far we know little if anything before inflation, as things were apparently infinite or at least our models break down there.

But in cyclic models of the universe, where the bang is finite and mathematically consistent, such information is available. One such model is the subject of a recent book: THE ENDLESS UNIVERSE, BY Paul Steinhardt and Neil Turok, 2007. I don't recall them specifically mentioning omega in the book.
 

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